The hydra was a one-headed monster but when iris cut off, 2 heads grow back in its place. If a hero tried to conquer it by cutting off its head every day, how many heads would the hydra have on the third day? And at the end of 10 days of trying to it?

3 days: 8 heads.

10 days: 1024 heads.

Step-by-step explanation:

If each time the hero cuts off all the heads, then the amount doubles each time. This can also be represented using powers of 2, with 2^n, where n is the number of days.

2^1 = 2, so two heads the first time he cuts it.

2^2 = 4, so four heads the second time he cuts it.

With three, 2^3 is 8 so there are 8 heads.

With ten, 2^10 is 1024 so there are 1024 heads.